\(h > 0\)  is a smoothing parameter and \(\Vert \cdot \Vert _p\)  is the \(\ell _p\)  norm. The precise reason for using the weighted \(\ell _1\)  norm in (REF ) is that its proximal map has a closed form solution. Note that the weights in (REF ) are similar to that used in nonlocal means [1]}.
